Answer:
B. The graph is incorrect and the line should go through the point (3, 13.5)
Step-by-step explanation:
The equation is y = 4.5x
y = the y-axis/dependent variable
x = the x-axis/independent variable
4.5 x 1 = 4.5
4.5 x 2 = 9
4.5 x 3 = 13.5
Therefore the written ordered pairs would look like this.
(1, 4.5)
(2, 9)
(3, 13.5)
In the graph, (3, 13.5) is graphed as (13.5, 3) making the graph incorrect.
The statement which is true about the graph shown is that: the graph is incorrect and the line should go through the point (3, 13.5).
How to interpret the graph?Generally speaking, the graph of any linear function is always modeled by a straight line and it indicates a proportional relationship because it starts from the origin (0, 0).
Mathematically, a proportional relationship can be represented or modeled by the following linear equation:
y = kx
Where:
k represents the constant of proportionality.x and y represents the data points, variables, or coordinates.At data point (4.5, 4.5), we have:
y = 4.5x
y = 4.5(4.5)
y = 20.25 (incorrect).
At data point (3, 13.5), we have:
y = 4.5x
y = 4.5(3)
y = 13.35 (correct).
Therefore, we can logically deduce that this graph is incorrect because its line didn't pass through the data point (3, 13.5).
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determine the answer to the nearest tenth of a percent.12 out of 52 cards in a deck are face cards.What percentage of cards in a deck are face cards?
Total number of cards: 52
Number of face cards: 12
To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:
[tex]\frac{12}{52}\times100[/tex]The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.
Solving the operations:
-solving the division
[tex]0.2308\times100[/tex]-solving the multiplication:
[tex]23.08[/tex]The face cards represent 23.08%.
Rounding to the nearest tenth of a percent (one decimal place):
[tex]\approx23.1[/tex]Answer: 23.1%
Mrs. Smith spent $50 more at a store than mrs. Jones. Combined they spent at most $250. What is the most they each could have spent?
By working with inequalities, we will see that:
Mrs. Jones can spend between $0 and $100.Mrs. Smith can spend between $50 and $150.How much each spent?Let's define:
S = amount that Mrs. Smith spent.J = amount that Mrs. Jones spentWe know that Mrs. Smith spent $50 more at a store than Mrs. Jones, then:
S = J + 50
And together they spent at most $250, then:
S + J ≤ 250
Now, replacing the equation in the inequality, we get:
(J + 50) + J ≤ 250
2*J + 50 ≤ 250
2*J ≤ 250 - 50
2*J ≤ 200
J ≤ 200/2
J ≤ 100
So Mrs. Jones spent at most 100 dollars.
And Mrs Smith spent $50 more than that, so we can write the inequality.
50 ≤ S ≤ 150
She spends between $50 and $150.
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A cyclist rides her bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate:km/hDistance traveled in 2 hours:km
Given:
1 mile = 1.6 km
So, 8 miles per hour in kilometers per hour is given by:
[tex]\frac{1}{8}=\frac{1.6}{x}[/tex]Where x = # of kilometers
So, solve for x:
[tex]\begin{gathered} x\cdot1=1.6\cdot8 \\ x=12.8 \end{gathered}[/tex]This is 12.8 km per hour
Next, the distance traveled in 2 hours is:
[tex]rate=\frac{distance}{time}\rightarrow distance=rate\times time[/tex]Substitute the values:
[tex]distance=12.8\times2=25.6[/tex]Answer:
Rate: 12.8 km/h
Distance traveled in 2 hours: 25.6 km
Distribution Whole Number Multiple Choice
Distribution of
a(b + c) = ab + ac
Then
36 + 12 is equivalent to
Find composed numbers
36= 3•12
12 = 3•4
THEN ANSWER IS
3• (12 + 4)
The slant height and the base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
The most appropriate choice for cone and total surface area of cone will be given by-
Total surface area of the cone is [tex]198235.71 cm^2[/tex]
What is cone and total surface area of cone?
Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.
Cone is obtained by revolving a right angled triangle about one of its legs.
Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.
If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by
[tex]\pi r(r+l)[/tex]
Here
Ratio of the slant height and radius of base of the cone = 2:1
Radius = 145cm
Slant height = [tex]145 \times 2[/tex]
= 290 cm
Total surface area of cone = [tex]\pi r(r+l)\\[/tex]
= [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]
= [tex]\frac{22}{7} \times 145 \times 435[/tex]
= [tex]198235.71 cm^2[/tex]
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Complete Question
The slant height and the radius of base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?
In the circle below, the central angle is measured in radians.When rounded to the nearest .01 of a centimeter,the length of arc Sis?? cm?
Length of the given arc
[tex]\begin{gathered} l=r\theta \\ =2\times\frac{\pi}{4} \\ =\frac{\pi}{2} \\ =\frac{22}{14} \\ =1.571 \\ =1.57 \end{gathered}[/tex]So the length of the given arc is 1.57 cm
Part A: On the imagePart B: What is the answer of k?
The effect on the graph replacing f(x) by f(x)+k is a vertical shift k units.
According to the graph the resulting function is 2 units higher from the original one. This means k has a value of 2.
Solve each system of equations please show your work! 3x+y-2z=22 x+5y+z=4 x=-3z
The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The system of the equations are,
3x + y - 2z = 22 .... (i)
x + 5y + z = 4 .... (ii)
x = - 3z .... (iii)
Now,
Solve the equations as;
Substitute x = - 3z in both equations, we get;
⇒ 3x + y - 2z = 22
⇒ 3 × -3z + y - 2z = 22
⇒ - 9z + y - 2z = 22
⇒ - 11z + y = 22 .... (iii)
And, x + 5y + z = 4
- 3z + 5y + z = 4
5y - 2z = 4 ... (iv)
Solve equation (iii) and (iv) we get;
⇒ y = 44 and z = 2
So, x = - 3z
⇒ x = - 3 × 2
⇒ x = - 6
Thus, The solution of the system of equations are;
⇒ x = - 6 , y = 44 and z = 2
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Graph 5x + y = 3x + 2(a) Rewrite the equation in slope intercept form. Show your work.(b) Graph the line. If you aren't able to draw on the graph using the technology you have available,then just describe it in words - tell where it is located
Given the Linear Equation:
[tex]5x+y=3x+2[/tex](a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you get:
[tex]\begin{gathered} y=-5x+3x+2 \\ y=-2x+2 \end{gathered}[/tex]Notice that:
[tex]\begin{gathered} m=-2 \\ b=2 \end{gathered}[/tex](b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:
[tex]b=2[/tex]Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":
[tex]y=0[/tex]Because the value of "y" is zero when the line intersects the x-axis.
Therefore, you get:
[tex]\begin{gathered} y=-2x+2 \\ 0=-2x+2 \\ -2=-2x \\ \\ \frac{-2}{-2}=x \\ \\ x=1 \end{gathered}[/tex]Now you know that the line passes through these points:
[tex](1,0),(0,2)[/tex]Hence, you can graph it.
Therefore, the answers are:
(a) Equation in Slope-Intercept Form:
[tex]y=-2x+2[/tex](b) Graph:
what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We have to determine the lcm of the rational algebraic equation
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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(2 3/5) Multiply (-2 2/3)
[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]
ATTACHED IS THE SOLUTION
Answer:
(-104/15)
Step-by-step explanation:
3 2
2 ------ × -2 -------
5 3
5 × 2 = 10
10 + 3 = 13
3 × -2 = -6
-6 + -2 = -8
13 -8 104
------- × ------- = (-) -------
5 3 15
I hope this helps!
I need to know the answer but I need to know how to get it and work it out
Let's start by completing the first table.
The questions gives the depth in two times:
- 2 hours after start -> 64 inches of water
- 4 hours after start -> 48 inches of water
From this, we can identifythe units:
- for time, we will use hours
- for depth, we will use inches
The first given values are:
- for time, 2
- for depth, 64
The second given valuesa are:
- for time, 4
- for depth, 48
So, the table is:
Quantity Name | Time | Depth of Pool
Unit | hour | inch
Given Value 1 | 2 | 64
Given Value 2 | 4 | 48
Now, we need to calculate the slope, which can be done using the given points and the equation:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{48-64}{4-2} \\ m=\frac{-16}{2} \\ m=-8 \end{gathered}[/tex]So, the slope is -8 inches per hour.
The interceptwe the b in the equation:
[tex]y=mx+b[/tex]Where y is the depth and x is the time. So, using the first given values and the slope, we can find b:
[tex]\begin{gathered} 64=-8\cdot2+b \\ 64=-16+b \\ b=64+16 \\ b=80 \end{gathered}[/tex]Thus, the intercept is 80 inches.
So, the formula we have for the pump is:
[tex]y=-8x+80[/tex]Using it, we can answer questions 1 and 2:
1. After 6 hours means x = 6, so:
[tex]\begin{gathered} y=-8\cdot6+80 \\ y=-48+80 \\ y=32 \end{gathered}[/tex]So, y = 32, thus, the depth of the water will be 32 inches.
2. The level 24 inches mean y = 24, so:
[tex]\begin{gathered} 24=-8x+80 \\ 8x=80-24 \\ 8x=56 \\ x=\frac{56}{8} \\ x=7 \end{gathered}[/tex]Thus, x = 7, and the water will be at 24 inches after 7 hours.
Please help I did help
The scientific notation of the expression is as follows:
(7 × 10⁻⁶) (7 × 10⁻⁶) = 4.9 × 10⁻¹¹(3.76 × 10⁵) + (7.44 × 10⁵) = 1.12 × 10⁶How to solve expression in scientific notation?The proper format for scientific notation is a x 10ᵇ where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
Scientific notation is a special way of writing numbers.
The expression can be express in scientific notation as follows:
Therefore,
(7 × 10⁻⁶) (7 × 10⁻⁶)
Hence, we have to multiply the integers and add the exponents as follows:
(7 × 7) × (10⁻⁶. 10⁻⁶)
49 × 10⁻⁶⁻⁶
49 × 10⁻¹²
4.9 × 10⁻¹¹
Hence, the second can be express in scientific notation as follows:
(3.76 × 10⁵) + (7.44 × 10⁵)
(3.76 + 7.44) × 10⁵
11.2 × 10⁵
1.12 × 10⁵⁺¹
1.12 × 10⁶
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Write a sequence of transformations that takes A to A'.
A rotation of 270 degrees about the origin would transform the figure as follows:
Which does not maps the A to A'.
Now, one sequence of transformations that take A to A' is:
1)First, a reflection over the x-axis would transform the figure as follows:
2) We translate the figure 3 units up and 4 units to the right:
Answer: Reflection over the x-axis, translation 3 units up and 4 units to the right.
A brick has dimensions of110. cm x 655 cm x 1330 cm.What is the volume of the brick incubic meters?[?] m3Recall that 1 cm =10-2 mGive your rounded answer to the correct number ofsignificant figures.Volume, cubic metersEnter
The dimension of the brick is given 110 cm x 655 cm x 1330 cm.
We know that 1 cm = 10^-2 m.
So, the dimensions of brick in meters will be 1.10 m x 6.55 m x 13.30 m.
The volume of the brick is calculated below:
[tex]\begin{gathered} V=1.10\times6.55\times13.30 \\ =95.8265m^3 \end{gathered}[/tex]Thus, the volume of the brick in cubic meters is 95.8265 m^3.
Real world compositionsShoe sizes are marked differently in many countries. In Japan, a shoe size is 16 more than the size in the United States. In Korea, a shoe size is 224 more than the size in Japan. Determine the function of the U.S. size of a shoe in terms of the shoe size in Korea. What is the U.S. shoe size of a shoe that is 250 in Korea? Solve using composite functions
To solve this exercise, we define the following variables:
• j = Japan size of shoes,
,• u = United Sates size of shoes,
,• k = Korea size of shoes.
From the statement of the problem, we know that:
0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,
,1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.
We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).
1) From point 1, we have:
[tex]\begin{gathered} j=16+u, \\ u=j-16. \end{gathered}[/tex]2) From point 2, we have:
[tex]\begin{gathered} k=224+j, \\ j=k-224. \end{gathered}[/tex]Replacing the expression of j in terms of k in the expression of u, we get:
[tex]u=j-16=(k-224)-16=k-240.[/tex]Replacing the value k = 250 in the last equation, we get:
[tex]u=250-240=10.[/tex]Answer
The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.
Use 2 methods to predict the output for an input of 200.
Given a table represents a relation between x and y
As shown, the change of (x) and (y) vary with a constant rate
So, the table represents a linear function
The general equation will be: y = m * x + b
where (m) is the slope, (b) is the value of y when (x=0)
So, from the table, when x = 0 , y = 25
The slope will be as follows:
[tex]m=\frac{30-25}{1-0}=\frac{5}{1}=5[/tex]So, the equation will be:
[tex]y=5x+25[/tex]When the input = 200, x = 200
So, substitute with (x) to find the output (y)
[tex]y=5\cdot200+25=1000+25=1025[/tex]So, the answer will be:
For an input 200, the output is 1025
===================================================
Another method to solve using the arithmetic sequence.
As shown in the table consider (x) represents the number of terms
So, (y) will be an arithmetic sequence
The first term = a = 30
The common difference = d = 35 - 30 = 5
the general rule of the arithmetic sequence is:
[tex]y_{}=a+d(x-1)[/tex]substitute with (a) and (d)
[tex]y=30+5(x-1)[/tex]When x = 200
[tex]y=30+5(200-1)=30+5\cdot199=1025[/tex]So, for an input 200, the output = 1025
Solve the equation for all values of x.
|5x + 8| 8 = 3x
It takes 4 oranges to makes 6 ounces of orange juice. What are the two unit rates?
Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.
Step-by-step explanation:
Amanda and Jeremiah are standing on the same side of a large lake. They are separated by a horizontal distance of 4000 ft. Both Amanda and Jeremiah can see a helicopter that is directly above the horizontal distance between them. Amanda’s angle of elevation to see the helicopter is 60 and Jeremiah’s angle of elevation to see it is 30. 1.What is the distance between Amanda and the helicopter?
Explanation: First of all we need to know if our triangle is a right triangle (has one 90° inner angle) to be able to use the law of sines to calculate the distance between Amanda and the helicopter.
Step 1: Once we know that the sum of all inner angles of a triangle is equal to 180° we can calculate the unknown angle as follows
As we can see above the missing inner angle is 90° which means it is a right triangle.
Step 2: Now we can use the law of sines as follows
once sin (90°) = 1 and sin (30°) = 0.5, let's calculate "x" below
[tex]\begin{gathered} \frac{x}{sin(30)}=\frac{4000}{sin90} \\ x=\frac{4000*0.5}{1} \\ x=2000ft \end{gathered}[/tex]Final answer: As we can see above, the final answer is 2000 ft
ASAP!!!!
PLEASE HELP!!!
When a whole number is multiplied by 10 to the power of 2, how does the placement of the decimal point change?
a) It moves two places to the right.
b) It moves ten places to the right.
c) It moves two places to the left.
d) It moves ten places to the left.
Answer: A) moves two places to the right
Example:
[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]
The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.
Under his cell phone plan, Deion pays a flat cost of $39 per month and $4 per gigabyte. He wants to keep his bill at $49.40 per month. How many gigabytes of data can he use while staying within his budget?
Answer:
(49.4 - 39) / 4
= 10.4 / 4
= 2.6GB
Step-by-step explanation:
From the diagram below, what is the measure of the angle of depression from point A
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.
Thus, the angle of depression is 45°
∠A and \angle B∠B are vertical angles. If m\angle A=(x+12)^{\circ}∠A=(x+12)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the measure of \angle B∠B
Measure of ∠B = 16°
∠A and ∠B are Vertical angles with ∠A = x+12° and ∠B = 6x-8°.
Vertical angles are angles formed between two lines at the intersection of them and are opposite to each other.
Also measures of Vertical angles are equal.
Now to find the measure of ∠B, we need to find x.
So here, ∠A = ∠B
⇒ x+12° = 6x-8°
⇒ 6x - x = 12 + 8
⇒ 5x = 20
⇒ x = 4
Hence, ∠B = 6x-8° = 6 x 4 -8 = 16°
So measure of ∠B = 16°
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Luna brought all her savings with her to Rome, in euros. For the first week, she spent the same amount of money each day. The table shows how much Luna had left at the end of each day. What was the initial value of Luna's savings? Day Euros ? 315 1 2 280 3 245 4 210 5 175 6 140 7 105 35 euros 315 euros 80 euros 350 euros
every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350
Therefore, the initial value was $350
Carefully follow the steps to find the solution to the three equation system.
a. Use equations 2 and 3 and eliminate the by multiplication and addition, creating a new equation with only two variables.
b. Use equations 1 and 2 and eliminate the by multiplication and addition, creating a second equation with only two variables.
c. Use the two new equations, and eliminate the -variable by multiplication and addition, finding the value for the -variable.
d. Substitute -value in the second new equation and find the -value.
e. Substitute the and values into original equation 2 to find the -value
(-2,-5,-3)
(1,4,2)
(-4,1,-2)
(1,2,4)
(2,5,3)
Answer:
The answer is (1,4,2)
Using the bankers rule, find the simple interest on 18,000 pesos at 17.25% from Feb.4 to Apr 21 of the same leap year.
From the question
By the bunkers rule
[tex]I=\text{PRT}[/tex]P = 18,000
R = 17.25% = 0.1725
For the time
Since the year is a leap year then
February has 29 days
Hence
From Feb.4 to Apr 21 implies
The number of days left in Feb. = 25
Number of days in March = 31
Number of days for April = 21
Therefore, Total number of days = 25 + 31 + 21 = 77
By Bankers rule, total days for the year will be 360
Hence the interest is
[tex]\begin{gathered} I=18000\times0.1725\times\frac{77}{360} \\ I=18000\times0.1725\times0.2139 \\ I=664.16 \end{gathered}[/tex]Therefore, the interest is 664.16
please helpppppppppppppp
Answer:
Step-by-step explanation:
Substitute a and b with 1/4 and 6
5b/ 32a^2
5(6)/ 32(1/4)^2
30/32(1.96)
30/62.72
0.5102 Answer
Ben is a coal miner and spends most of his workday in an underground mine. Which is the most likely depth he is at while doing his job?
Answer:-900 feet. I think this is correct so don't use it unless you think its right
Step-by-step explanation:
72b384 is a number in which one of its digits is 'b'. if the number is a multiple of 9, what is the numerical value of 'b'?
Answer:
3
Step-by-step explanation:
Hello!
A simple way to find if the number is a multiple of 9 is if the sum of the digits in the number is a multiple of 9, then the number itself is a multiple of 9.
So that means: 7 + 2 + b + 3 + 8 + 4 is a multiple of 9
If we add it up we should get: 24 + b
The multiples of 9 include 9,18,27,36,45,54....., and the closest multiple of 9 to 24 is 27. Therefore, the missing digit should be 3, as 27 - 24 is 3.
The next closest numbers would be 18 and 36, but you would need to add a negative number to get 18, and a two-digit number to get 36.